Hi Kelly
I can only reproduce this if one of the sections in my Map Journal has an usually long title with no spaces in it. For example if the title of my section is that long Hawaiian fish name (humuhumunukunukuapuaa) it partially clips the Delete icon but I can still click it. Does one of your section titles perhaps start with a long word with no spaces in it? If so, editing that title to break up that first word, and then going back to the Organize dialog should let you access the Delete button.
If that isn't what is going on, could you also let us know which web browser you are using and also which operating system (Windows 10, etc).
Rupert